Quartic equation

A quartic equation is the result of setting a quartic function to zero, an example quartic equation is the equation

2x⁴+4x³-26x²-28x+48=0,

the general form is

a₄x⁴+a₃x³+a₂x²+a₁x+a₀=0, and a₄≠0.

A quartic equation always has 4 solutions (or roots).They may be complex or there may be duplicate solutions.

It is the highest degree of polynomial equation for which exact values of the roots can be found, by taking nth roots, and use of the normal algebraic operators.

If a₀=0, then one of the roots is x=0, and the other roots can be found, by dividing by x, and solving the resulting cubic equation, a₄x³+a₃x²+a₂x+a₁=0.

Otherwise, divide the equation by a₄, to get an equation of the form

x⁴+ax³+bx²+cx+d=0.

Substitute x=t-a/4, to get an equation of the form

t⁴+pt²+qt+r=0.

Then find the roots somehow. (To be written.)

See also

• linear equation,
• quadratic equation,
• cubic equation,
• quintic equation